www.postersession.com Students who complete their K-12 schooling by attending one elementary, one middle, and one high school are the exception rather than the rule in U.S. public schools today. Not including normative school changes such as those from elementary to middle school, most students change schools at least once during their K-12 school careers (Rumberger, 2002). The independent negative effect of mobility on math and reading scores and dropout rates, controlling for student background and prior achievement, has been estimated to be about one-third of a standard deviation, a moderately substantial effect (Reynolds, Chen & Herbers, 2009). However, most research on mobility has been limited by analytic methods that do not adequately control for the multiple sources of variation in achievement (student fluctuations over time, differences between students and schools) or students’ membership in multiple schools over time. Prior research has also failed to account for the reasons students move. All school transfers can be conceptualized in reference to whether or not they are triggered by other changes in the student’s environment (Bronfenbrenner, 1979) – residential changes, changes in students’ academic “fit” (e.g., switch to private or special school) or changes in family structure or environment (e.g., divorce, parental job loss, eviction) (see Figure 1). Conclusions Using Cross-Classified Multiple Membership Growth Curve Modeling in Non-Hierarchical Multilevel Data Structures: The Effect of School Mobility and Concurrent Changes on Students’ Academic Achievement Bess A. Rose Johns Hopkins University School of Education References Bronfenbrenner, U. (1979). Contexts of child rearing: Problems and prospects. American Psychologist, 34, 844-850. Browne, W. J. (2014). MCMC estimation in MLwiN version 2.31. Centre for Multilevel Modelling, University of Bristol. Grady, M. W., & Beretvas, S. N. (2010). Incorporating student mobility in achievement growth modeling: A cross-classified multiple membership growth curve model. Multivariate Behavioral Research, 45, 393-419. Hanushek, E. A., Kain, J. F., & Rivkin, S. G. (2004). Disruption versus Tiebout improvement: The costs and benefits of switching schools. Journal of Public Economics, 88, 1721–1746. Rasbash, J., Browne, W. J., Healy, M., Cameron, B., & Charlton, C. (2014). MLwiN Version 2.31. Centre for Multilevel Modelling, University of Bristol. Reynolds, A. J., Chen, C.-C., & Herbers, J. E. (2009, June). School mobility and educational success: A research synthesis and evidence on prevention. Paper presented at the Workshop on the Impact of Mobility and Change on the Lives of Young Children, Schools, and Neighborhoods, National Research Council, Washington, DC. Rogers, L. (2004). Student mobility in Maryland: A report to The Annie E. Casey Foundation. Baltimore, MD: Maryland State Department of Education. Rumberger, R. W. (2002). Student mobility. In Encyclopedia of Education (2nd ed., Vol. 7, pp. 2381-2385). New York: Macmillan Reference USA. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University. In general, students’ GPAs decline over the course of their schooling. The average first-grade GPA, adjusting for student characteristics, school membership, and mobility, is about 3.22 on a 4-point scale. Non-mobile students lose about 0.13 GPA points per year as they progress through school after first grade. There are immediate and persistent effects of school changes on GPA. A student who changes schools once in a given year is predicted to lose 0.08 GPA points that year, and another 0.08 points each year thereafter. However, students are less affected by mobility as they grow older, as indicated by the positive and significant interaction terms. These effects vary depending on the reasons students change schools. The overall negative immediate effect of current-year mobility appears to be driven by Type 3 and Type 4 moves (changes in educational settings; residential moves accompanied by other family changes) as well as moves for which the reason is unknown. The overall negative persistent effect also appears driven by these types of moves as well as by Type 2 moves (residence-only moves). Type 1 school changes (e.g., redistricting, school closure) do not have any significant effects on GPA, either immediately or long term. However, the relatively small number of transfers in this category likely limited the study’s power to detect effects. Type 2 school changes (residence-only moves) do not have significant immediate effects, but they do have negative persistent effects of about .04 GPA points. Type 3 changes (educational settings) have an immediate negative impact of .09 GPA points; the persistent effects of Type 3 changes are also worse than Type 2 changes (˗0.08 GPA points), but both types of effects are less harmful in later years of schooling. Type 4 school changes (residential moves accompanied by other family changes) are the most harmful, both in terms of immediate impact (˗0.11) and persistent effects (˗0.1β), but older students are less affected by these types of moves. Introduction Results Abstract This study examined the differential effects of school transfers on achievement, depending on whether the student also experienced changes in educational, neighborhood, or family environments when transferring. Because students usually belong to multiple schools over their educational history (and sometimes multiple schools within a school year), cross-classified multiple membership growth curve modeling (CCMM-GCM) was used to model academic achievement over time. First-grade GPA was a function of the school(s) attended during the first year of school; annual change in GPA was a function of first-year school(s) and subsequent school(s). Results indicate that transfers are more harmful when concurrent changes occur in students’ educational, neighborhood, or family environments. Residential Environment No Change Change Other Environment No Change TYPE 1 District decision about school boundaries, rezoning, school closure n=218 (3.0%) TYPE 2 Residential move with no other family changes n=1902 (26.4%) Change TYPE 3 Change in program due to parent choice or school decision for better fit n=1006 (14.0%) TYPE 4 Residential move with family change such as divorce, foster care, job loss, eviction n=1817 (25.2%) Figure 1. Reasons for Mobility Total number of school changes = 7200. An additional 2257 school changes (31.3%) were due to unknown reasons. Note. School histories were examined from first grade onward, since mandatory all-day kindergarten was not yet in effect when these students entered school. School histories included in-state, out-of-state, public and private schools. Students with incomplete school histories were significantly more likely to be mobile than students with complete histories, χ 2 (1 df) = 540.03, p<0.000. Similarly, students lacking any report card records were also significantly more likely to be mobile than students with report card records, χ 2 (1 df) = 11.95, p<0.001. Methods The study used data records from a statewide representative sample (see Rogers, 2004) of 6,455 students having complete school histories and GPA data for at least one year, resulting in 43,812 repeated measures. Multilevel growth curve modeling was used in order to account for the repeated measures of students’ GPAs over time (Singer & Willett, β00γ). To account for students’ membership in multiple schools, a series of models were run based on the work of Grady and Beretvas (2010). However, a key difference in the present study’s data is that students could belong not only to multiple schools across years, but also to multiple schools within each school year. Thus, initial status (first grade GPA) was modeled as a function of not just the first school attended (as in Grady & Beretvas, 2010) but the set of schools attended during the first year of school (first grade). Change trajectories were modeled as a function of the set of first-year schools as well as the set of schools attended subsequently, just as in Grady and Beretvas (2010). Thus, the GPA in year t for student i who attended (the set of first-grade schools) j and (the set of subsequent schools) k was estimated as: GPA ti{j}{k} = π 0i{j} + π 1i Time ti{j}{k} + π 2i NewSchs_ThisYr ti{j}{k} + π 3i NewSchs_PriorYr ti{j}{k} + π 4i (NewSchs_ThisYr x Time) ti{j}{k} + π 5i (NewSchs_PriorYr x Time) ti{j}{k} + e ti{j}{k} where π 0i represents the student’s first-grade GPA (at time 0) and π 1i is the student’s annual change in GPA. π 2i represents the change in GPA for every new school the student enters each year (disruption effect) and π 3i is the change due to new schools in prior years (persistent effect) (Hanushek, Kain & Rivkin, 2004). π 4i and π 5i represent the changing effects of mobility as students age. Student covariates included free- or reduced-price lunch status, special education status, Limited English Proficient status, race, and gender. Year and retention variables were also included to account for the study’s panel design. School membership was cross-classified at Level 3 (first-grade schools and subsequent schools). Students could belong to multiple first-grade schools and multiple subsequent schools; membership was weighted based on the number of schools attended in a given year such that the weights summed to 1 each year. First-grade GPAs (at time 0) were modeled as a function of mean growth for all students in first-grade schools {j} plus random variation attributable to each first-grade school: ȕ 00{j} = Ȗ 000 + Σ h∈{j} w (3) tih u (3) 000h Changes in GPAs over time were modeled as a function of mean growth for all students in first-grade schools {j} and subsequent schools {k} plus random variation attributable to each first-grade school and each subsequent school: ȕ 10{j}{k} = Ȗ 1000 + Σ h∈{j} w (3) tih u (3) 000h + Σ h∈{k} w (4) tih u (4) 100h All other parameters were set as fixed. Finally, a second set of models estimated the specific effects of the 4 types of school changes by substituting the variables for school change types for the NewSchs variables. GPA ti{j}{k} = π 0i{j} + π 1i Time ti{j}{k} + π 2i Type1_ThisYr ti{j}{k} + π 3i Type1_PriorYr ti{j}{k} + π 4i (Type1_ThisYr x Time) ti{j}{k} + π 5i (Type1_PriorYr x Time) ti{j}{k} + π 6i Type2_ThisYr ti{j}{k} + π 7i Type2_PriorYr ti{j}{k} + π 8i (Type2_ThisYr x Time) ti{j}{k} + π 9i (Type2_PriorYr x Time) ti{j}{k} + π 10i Type3_ThisYr ti{j}{k} + π 11i Type3_PriorYr ti{j}{k} + π 12i (Type3_ThisYr x Time) ti{j}{k} + π 13i (Type3_PriorYr x Time) ti{j}{k} + π 14i Type4_ThisYr ti{j}{k} + π 15i Type4_PriorYr ti{j}{k} + π 16i (Type4_ThisYr x Time) ti{j}{k} + π 17i (Type4_PriorYr x Time) ti{j}{k} + π 18i Type9_ThisYr ti{j}{k} + π 19i Type9_PriorYr ti{j}{k} + π 20i (Type9_ThisYr x Time) ti{j}{k} + π 21i (Type9_PriorYr x Time) ti{j}{k} + e ti{j}{k} Models were analyzed using MCMC estimation in MLwiN v. 2.31 (Browne, 2014; Rasbash, Browne, Healy, Cameron, & Charlton, 2014). Acknowledgements Funding for the original study (Rogers, 2004) was provided by The Annie E. Casey Foundation. Funding for the current study was provided by a grant from the U.S. Department of Education’s Institute of Education Sciences (IES) to Johns Hopkins University’s interdisciplinary pre-doctoral research training program (R305B080020). Table 2. Estimated effects of school changes Model 1 Mobility Model 2 Reasons for Mobility Intercept at Grade 1 (GPA on 4-point scale) 3.226* (0.021) 3.223* (0.021) Immediate effect -0.076* (0.012) …due to Type 1 change 0.010 (0.075) …due to Type β change -0.020 (.024) …due to Type γ change -0.091* (0.036) …due to Type 4 change -0.105* (0.023) …due to unknown reasons -0.097* (0.022) Persistent effect -0.075* (0.008) …due to Type 1 change -0.013 (0.062) …due to Type β change -0.039* (0.019) …due to Type γ change -0.076* (0.029) …due to Type 4 change -0.120* (0.015) …due to unknown reasons -0.050* (0.015) Linear change Annual change -0.133* (0.004) -0.127* (0.004) Immediate effect x Time 0.011* (0.003) …due to Type 1 change -0.012 (0.016) …due to Type β change 0.006 (0.006) …due to Type γ change 0.015* (0.006) …due to Type 4 change 0.016* (0.006) …due to unknown reasons 0.009 (0.005) Persistent effect x Time 0.007* (0.001) …due to Type 1 change -0.015 (0.009) …due to Type β change 0.003 (0.003) …due to Type γ change 0.014* (0.004) …due to Type 4 change 0.012* (0.002) …due to unknown reasons 0.001 (0.002) Note. Parameter estimates are unstandardized. SEs are in parentheses. * p < .05 Accounting for the reasons for mobility improves model fit. Results of the CCMM are displayed in Table 2. Examination of the variance components (Table 1) confirms the need for CCMM-GCM to account for the cluster effects of repeated measures and school membership. About 50 percent of the total variance in GPAs is due to within-student fluctuation. While most (72 percent) of the variation among first-grade GPAs (intercepts) is due to differences between students, 28 percent is due to differences between first-grade schools. Similarly, while differences between students account for some of the variation among GPA trajectories (38 percent), first-grade schools account for 13 percent and subsequent schools account for 50 percent of the variance in slope. Table 1. Variance components Model 1 Mobility Model 2 Reasons for Mobility Within student .244 (.002) .243 (.002) Between students First-grade GPA .167 (.006) .167 (.005) Change in GPA .006 (.000) .006 (.000) First-grade schools First-grade GPA .065 (.006) .066 (.006) Change in GPA .002 (.000) .002 (.000) Subsequent schools First-grade GPA N/A N/A Change in GPA .008 (.001) .008 (.001) Model fit statistic (DIC) 70018.89 69978.39 pD 7577.72 7597.62 Note. Standard errors are in parentheses.